Welcome to the hobby! Definitely a lot of fun, especially when you get to drink the results of your labor.
Yes, you can use a juicer. When you start doing larger quantities you will probably want something bigger like an actual apple press, but for just one gallon a counter top juicer will work fine.
ALWAYS wash your apples with water before pressing. You never know what else might be on the surface of the apples. I thoroughly wash all of my apples with a pressure washer before pressing. I do many wild fermentations with apples, and there is still plenty of active yeast for wild fermentation after washing. My unconfirmed belief is that there are also active yeast colonies in the core of the apple.
A wild ferment is quite simple. Step-by-step instructions are below the other answers to your questions.
Typically, the best ciders seem to come from apples that are not necessarily the tastiest when you bite into them. The sweetness that dominates most "Handfruit" and "Dessert" varieties end up fermenting out, and makes for a bland cider. Look for varieties with some bitter, sharp, sour, earthy, spicy, other qualities besides sweet. Those flavors are what will remain in your finished cider. It can be tough to find a single variety that fits the need, so many people tend to blend different apple varieties to find the taste they are looking for.
If you live in an apple growing region as I do (pacific Northwest for me), then I simply go the "door knocking" route, rather than going to orchards and paying for apples. It blows me away how many people plant apple trees and then never do anything with them. If I see a house with an apple tree that does not appear to be used, then I knock and ask if I can pick their tree. I always clean up and dispose of the groundfall, and also give them some of either the Juice or the finished cider when done. I haven't paid for an apple or juice in years.
Instructions for wild fermentation Apple Cider:
1) Turn apples into Juice. Do not pasteurize and do not add any Campden/K-Meta/Sulfites.
Note: If you want a Sparkling Cider, then set aside 10% of your juice in the freezer for use at the very end of the process (more on that later).
2) Measure the starting gravity of your Juice (optional, but necessary if you want to have any idea of your alcohol content).
3) Immediately after Juicing, pour Juice into a sterilized container (Primary) and attach airlock. This container should have some extra headspace to allow for krausen/foaming that occurs during the fermentation process.
4) Wait. Observable Airlock activity from a wild fermentation will typically start anywhere from 1-5 days from juicing. If you still have not observed any airlock activity after 5 days, then you may want to Pitch yeast (yes, this means you no longer have a wild fermentation, but is better than wasting good fresh pressed juice).
5) Optional: You can add yeast nutrient 1-2 days after observable airlock activity begins, if desired. (Note: I only use organic yeast nutrient on wild fermnations [Fermaid-O])
6) Continue waiting. Depending on different factors fermentation will take anywhere from 1-3 weeks, or potentially even longer.
7) When airlock activity has ceased, its time to rack to secondary. "Racking" is simply siphoning the liquid into a fresh, sterilized container. This gets the cider off of the dead yeast and apple solids that have settled to the bottom of your primary fermenter and allows for further clarification. This secondary fermenter should be smaller than your primary fermenter to limit the headspace. (Take a gravity reading at this point to verify that fermentation has proceeded as expected).
8) Wait for Cider to clarify. I like to wait until it is clear enough to read through, which typically takes 2-3 weeks in secondary.
9) Time to bottle. Measure the gravity again. It should be 1.000 or below at this point.
10a) If you want a Still (non carbonated) Cider, then simply siphon into sterilized bottles and seal them.
10b) If you want a Sparkling(carbonated) Cider then you will need to add Priming Sugar just before bottling. Rack the cider to another container and mix with your desired source of priming sugars. Since you said you did not want to add sugar, you can use that Juice that was set aside and frozen in step 1 as your source of priming sugars. By adding 10% of your total volume in fresh juice, that should bring your gravity to ~1.005, which I have found to give a very pleasant carbonation level. Siphon into bottles, then let the bottles sit to allow the residual yeasts to eat the priming sugars and carbonate your cider. I like to give at least 3 weeks of bottle conditioning to ensure full carbonation.
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